Very few can do this.
If you are able to do the following question, it shows you have a solid understanding of calculus.
Let g be a function and c a number in its domain. Suppose that
g′(c) = g′′(c) = g′′′(c) = 0 and g(4)(c) 0.(g(4) is the 4th derivative of g)
Prove that g attains a local minimum at c.

Question

Very few can do this.
If you are able to do the following question, it shows you have a solid understanding of calculus.
Let g be a function and c a number in its domain. Suppose that
g′(c) = g′′(c) = g′′′(c) = 0 and g(4)(c) > 0.(g(4) is the 4th derivative of g)
Prove that g attains a local minimum at c.

anonymous · Answer

attachment

anonymous · Answer

take a taylor series representation of g about c. g=g''''(c)*(x-c)^4/4!+O((x-c)^5).

anonymous · Answer

*expansion

anonymous · Answer

you dont have to use taylor series